ON THE SOLVABILITY OF DYNAMIC ELASTIC-VISCO-PLASTIC CONTACT PROBLEMS WITH ADHESION * Jiří Jarušek † Mircea Sofonea ‡ Abstract We consider a dynamic contact problem between an elastic-visco- plastic body and an obstacle, the so-called foundation. The contact is frictionless and is modelled with normal compliance of such a type that the penetration is restricted with unilateral constraint. The ad- hesion of contact surfaces is taken into account and the evolution of the bonding field is described by a first-order differential equation. We provide a weak formulation of the contact problem in the form of an integro-differential system in which the unknowns are the displacement, the stress and the bonding fields, then we present an existence result for the solution. We consider a sequence of penalized problems which have a unique solution, derive a priori estimates and use compactness properties to obtain a solution to the original model, by passing to the limit as the penalization parameter converges to zero. MSC: 74M15, 74H20, 49J40 keywords: elastic-visco-plastic material, dynamic process, frictionless contact, normal compliance, Signorini condition, adhesion, variational for- mulation, weak solution, a priori estimates * Accepted for publication in revised form on 12.08.09 † [email protected] Mathematical Institute, Academy of Sciences of the Czech Republic, Žitná 25, 115 67 Praha 1, Czech Republic ‡ [email protected] Laboratoire de Mathématiques, Physique et Systèmes, Uni- versité de Perpignan, 52 Avenue Paul Alduy, 66 860 Perpignan, France 191 Annals of the Academy of Romanian Scientists Series on Mathematics and its Applications ISSN 2066 - 6594 Volume 1, Number 2 / 2009
ON THE SOLVABILITY OF DYNAMIC ELASTIC-VISCO-PLASTIC CONTACT PROBLEMS WITH ADHESION
Jun 30, 2023
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